Estimating Multiple-

Discrete Choice Models:

An Application to

Computerization Returns

Presentation by Le Chen, Zhen Huo, Bernabe Lopez-Martin, Shihui Ma,

Naoki Takayama, and Andrew Triece

Motivation

The PC market is interesting from an IO perspective because it is characterized by rapid technological change and this technology can impact productivity in other markets

Firms purchase PCs from multiple brands, and they purchase multiple PCs from each brand (multiple-discreteness)

“Computerization Puzzle”: empirical finding that computerization has had no effect on firm productivity

Hendel's paper aims to incorporate the multiple-discreteness of the PC market into a model and estimate welfare gains from computerization

Basics

In Hendel's model, each firm has a number of potential tasks that can be performed by PCs and these tasks relate to the brands and quantities of PCs they demand

The model predicts that some firms will buy multiple brands of PCs and/or multiple units per brand depending on the tasks they need to perform

Based on the estimates of demand, return on investment on PCs in the banking industry is 92%, and an increase of 10% in the performance-to-price ratio of microprocessors is estimated to add 2.2% to end-user surplus

Multiple-Discreteness in the PC Market

Let F denote the number of firms, I denote the number of PC types.

Firms’ Tastes for Various Computer Attributes

Each PC is a bundle of N built-in attributes (ex: MHz, RAM, etc.).

One of the N attributes is considered to be an unobservable measure of “quality” of the type of PC.

Firm’s tastes over attributes are unobservable, hence can be treated as random variables.

These are denoted by:

Where there are N-1 built-in attributes and I dummies for PC type.

This vector Af is assumed to be multivariate normal.

Characteristics of the Firm

Let Df denote all the characteristics of firm f (size, sector, etc.)

Each firm can do up to Jf =Γ(Df) different tasks, where the number of tasks is a stochastic function of the firm’s characteristics.

Γ(Df) is assumed to be a Poisson distribution with parameter Λ(Df).

Firm seeks to maximize profit:

Key assumption: No inter-task externalities (profit in one task does not affect profit in another).

The Firm’s Problem

At the task level, the firm’s profit function is assumed to be of the following form:

Here, S(Df) is a return shifter and m(Df) is a taste shifter.

Assumption: PC types are perfect substitutes at the task level.

A firm will only use one PC type for each task.

What do we know?

Firm characteristics: D(f)

Firm PC purchases: Xf

What don’t we know?

The distribution of A and J, which is determined by the parameters θ

Note: We assume the distribution form,

but need to estimate the parameters

From the model, we know that the optimal purchases are

So we expect the firm to purchase:

The error term is given by the difference:

Suppose the assumed purchase process is true, then given the true parameter values:

Wecan generate the moment conditions

GMM method then can be implemented:

How to calculate the expected purchases: Simulation

Idea:

Suppose the parameters are given.

Given J, the number of tasks, draw many random variables from the distribution of A, and calculate the average.

Draw different numbers of tasks from Poisson process, repeat the procedure above, and calculate the average.

According to the existing work, when the number of random draws are large enough, the average from the simulation will equal to the true expected value.

Summary

1. Write down the observable numbers. 2. Given parameters, using simulation method,

find the expected purchase. 3. Using moments condition, calculate G(θ). 4. Repeat 2 and 3 until minimize G(θ), which

implies we find the true parameters.

Flow of Data

Pi

Ci

Df

Xf

Xf

Parameters

r.v.

e

Actual Data

Prediction GMM

Simulation

Data Sets

Prices and PC attributes

- from advertisements

- MHz, RAM and expandable RAM etc.

Actual behavior and characteristics of the establishments

- representative survey with questionnaire

- # of PC for each model and software etc.

- # of employees and white collars etc.

Explanatory Variables

empf = # of employees whf = # of white colors softf = # of different types of software dinsf = 1 if establishment f belongs to the

insurance sector dpif = 1 if firm f held in stock PCs i in the

previous year

Results

Distributional and functional forms.

Dummies control for unobserved quality differences (full set of brand dummies).

finsff

ffinsf

fff

dinsmwhmDm

empsdinsssDS

softgempgD

11

100

21

1)(

)(

)(

Asymptotic Chi-square test rejects the model; functional forms may not be sufficiently flexible.

Welfare gains from computerization: estimates of the profits of each establishment by using PCs represent 4.2% of total profits.

Return on investment is 92% (should be taken as an upper bound).

Some caveats.

Price aggregate demand elasticities (validity check if they imply reasonable substitution patterns).

Matrix of price elasticities: (1) all elements in the diagonal are negative, (2) larger substitution toward similar machines.

Potential biases.

1. Inter-task externalities (estimates would over-estimate per-task benefits).

2. Nonlinear pricing of PCs (large establishments get lower prices): they are actually willing to pay less for the PCs than the prices used in estimation.